ECSE-2100
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Fields and Waves I
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Professor Schubert
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2016 Spring Semester
Exam-01
1. Consider a 1st 50  transmission line (T-line), transmitting a sinusoidal signal with
wavelength , having a length of ℓ = 2, with an impedance-matched transmitter at one
end and an impedance-matched receiver at the other end. Next we connect a 2nd 50  Tline to the middle point of the 1st T-line. The 2nd T-line has various lengths and
terminations.
(a) Draw the experimental setup and label all objects appropriately.
(b) Assume that the 2nd T-line is lossless, has a length of ℓ = (1/4) , and is terminated by
an OC (open circuit). Describe how the signal at the receiver changes when connecting
the 2nd T-line.
(c) Assume that the 2nd T-line is lossy (so that the signal strength is negligible after having
propagated for a length of ℓ = 10 ), has a length of ℓ = 20 , and terminated by an SC
(short circuit). Describe how the receiver signal changes when connecting the 2nd T-line.
(d) Assume that the 2nd T-line is lossless, has a length of ℓ = (1/100) , and is terminated by
an SC. Describe how the receiver signal changes when connecting the 2nd T-line.
2. A sinusoidal 1 GHz wave propagating on a transmission line (T-line) has a wavelength of
 = 10 cm. Assume that the T-line is lossless and has a capacitance per unit length of C ’ =
150 pF/m.
(a) Calculate the phase velocity vphase, attenuation constant , phase constant , and
propagation constant ?
(b) Calculate the inductance per unit length, L’, of the T-line.
(c) Next, consider a different coaxial T-line; it is found to be too lossy for a certain
application. You are charged with re-designing the T-line. Which specific design changes
would you propose in order to improve the T-line?
3. The termination of a 50  transmission line (T-line) consists of a capacitor (C = 10 nF) in a
parallel circuit to an inductor (L = 10 nH).
(a) Draw the electrical circuit of the termination. Calculate the impedance of the
termination (symbolic expression).
(b) Determine the voltage reflection coefficient  at the angular frequencies  = 2f = 0 Hz,
100 MHz, and  Hz. Explain the results in your own words.
(c) Assume that a resistor R, in parallel to C and L, is added to the load. For  = 100 MHz,
qualitatively describe how the voltage reflection coefficient  changes.
4. Are the following statements (i) true, (ii) false, or (iii) impossible to determine due to lack of
information?
(a) A lossless transmission line with length of 7/4  that is terminated by an open circuit has
a voltage node at its front end that acts like a short circuit.
(b) For very long lossy T-lines, there is no or little effect of the termination (ZLoad) on the
input side of the T-line.
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